Chaos最新文献

In this paper, we introduce a Susceptible-Exposed-Infected-Recovered (SEIR) epidemic model and analyze it in both deterministic and stochastic contexts, incorporating the Ornstein-Uhlenbeck process. The model incorporates a nonlinear incidence rate and a saturated treatment response. We establish the basic properties of solutions and conduct a comprehensive stability analysis of the system's equilibria to assess its epidemiological relevance. Our results demonstrate that the disease will be eradicated from the population when R0<1, while the disease will persist when R0>1. Furthermore, we explore various bifurcation phenomena, including transcritical, backward, saddle-node, and Hopf, and discuss their epidemiological implications. For the stochastic model, we demonstrate the existence of a unique global positive solution. We also identify sufficient conditions for the disease extinction and persistence. Additionally, by developing a suitable Lyapunov function, we establish the existence of a stationary distribution. Several numerical simulations are conducted to validate the theoretical findings of the deterministic and stochastic models. The results provide a comprehensive demonstration of the disease dynamics in constant as well as noisy environments, highlighting the implications of our study.

The Atlantic Meridional Overturning Circulation (AMOC) stability landscape is commonly investigated with single-realization hysteresis diagrams driven by freshwater input in the North Atlantic Ocean. However, the effect of CO2 forcing on one side and the role of internal climate variability on the timing of tipping and the AMOC hysteresis on the other side remain less explored. Here, we address this gap by running three independent AMOC hysteresis simulations, consisting of a slow ramp-up plus ramp-down in the CO2 concentration (0.2 ppm/year) within the PlaSim-Large-Scale Geostrophic (LSG) intermediate complexity model. We show that the realizations of the CO2-driven hysteresis cycle, and particularly, the timing of the tipping and recovery, are remarkably affected by internal climate variability. In one of the three simulations, we even observe a reversed cycle, where the AMOC recovers at a higher CO2 level than at the collapse point. While statistical Early Warning Signals (EWSs) show some success in detecting the tipping points, we also find that the internal variability in the EWS considerably reduces the predictability of collapse and leads to false positives of an approaching AMOC tipping. We suggest that the AMOC collapse in the presence of internal climate variability may have characteristics that deviate substantially from the behavior seen in simple models and that caution is needed when interpreting results from a single-experiment realization. Our findings highlight the need for a probabilistic approach in defining a "safe operating space" for AMOC stability, since it might not be possible to define a single critical CO2 threshold to prevent AMOC collapse.

At present, the research on the dynamics of cooperative behavior of agents under reinforcement learning mechanism either assumes that agents have global interaction, that is, agents interact with all other agents in the population, or directly study the influence of relevant factors on cooperation evolution based on the local interaction in a network structure. It neglects to formally study how the limitation of agents that only interact with local agents affects their strategy choice. Thus, in this paper, we study the cooperative behavior of agents in a typical social decision-making environment with conflicts between individual interests and collective interests. On the one hand, a programmed game model in game theory, namely, prisoner's dilemma game, is used to capture the essence of real-world dilemmas. On the other hand, the effects of local and global strategy learning on the cooperative evolution of agents are investigated separately, and the nature of spatial reciprocity under the reinforcement learning mechanism is found. Specifically, when there is no inherent connection between the interacting agents and the learning agents within the system, the network structure has a limited effect on promoting cooperation. It is only when there is an overlap between the interacting agents and the learning agents that the spatial reciprocity effect observed in the traditional evolutionary game theory can be fully realized.

We propose a nonlinear FitzHugh-Nagumo neuronal model with an asymmetric potential driven by both a high-frequency signal and a low-frequency signal. Our numerical analysis focuses on the influence of a state-dependent time delay on vibrational resonance and delay-induced resonance phenomena. The response amplitude at the low-frequency signal is explored to characterize the vibrational resonance and delay-induced resonance. Our results show that for smaller values of the amplitude of the state-dependent time-delay velocity component, vibrational resonance and multi-resonance occur in the neuronal model. For large values of the high-frequency excitation amplitude, vibrational resonance appears with one peak. Furthermore, we observe a change in the response when the amplitude of the state-dependent time-delay velocity component increases. In addition, we analyze how the state-dependent time-delay position and velocity components can give birth to delay-induced resonance for separate and together. The key findings of this work demonstrate that the state-dependent time-delay velocity component plays a crucial role in both phenomena. Specifically, the delay parameter serves as a critical control factor, capable of triggering the onset of the two resonances.

We consider the standard nontwist map with strong dissipation that leads the system to a 1D circular map with a quadratic sinusoidal oscillation and two control parameters. The 2D Lyapunov and isoperiodic diagrams reveal a complex interplay between domains of periodicity embedded in regions dominated by quasiperiodic and chaotic behaviors. Arnold tongues and shrimp-like, among other sets of periodicities, compose this rich dynamical scenario in the parameter space. Cobwebs and bifurcation diagrams help reveal the behavior of attractors, including multistability, period-doubling, pitchfork bifurcations, as well as boundary, merging, and interior crises that influence the structures of periodicity. Furthermore, we bring to light the global organization of shrimp-like structures by carrying out a new concept of orbits, the extreme orbits, and announce that the fractal dimension, believed to be universal in the parameter space for decades, has its symmetry breaking in the vicinity of shrimp-like cascades.

Unlike hollow triangles formed through pairwise interactions, a filled triangle or two-simplex comprises three nodes that form a group and represent the most fundamental higher-order interaction. To analyze the effects of higher-order triangles on the robustness of world trade networks, we integrate multilateral regional trade agreements and import-export world trade data to construct two-simplex higher-order trade networks. The topological characteristics indicate a significant growth in the scale and complexity of trade networks over time, with a notable decline in 2020. Then, we introduce node attack strategies designed to simulate scenarios where the key countries or regions withdraw from the trade network. It is revealed that network robustness has improved along with size and complexity, although it diminished in 2020. To further explore the factors influencing the changes in network robustness, we generate higher-order synthetic trade networks based on the random simplicial complex (RSC) model and the scale-free simplicial complex (SFSC) model. The synthetic trade networks demonstrate that increasing the average degree enhances robustness, while merely increasing the number of nodes or filled triangles can weaken it. Additionally, scale-free higher-order networks exhibit lower robustness due to vulnerability of the hub nodes, in contrast to the higher resilience of random simplicial complexes. These insights emphasize the importance of fostering multilateral interactions and strengthening ties for network robustness.

The global stability of oscillator networks has attracted much recent attention. Ordinarily, the oscillators in such studies are motionless; their spatial degrees of freedom are either ignored (e.g., mean field models) or inactive (e.g., geometrically embedded networks like lattices). Yet many real-world oscillators are mobile, moving around in space as they synchronize in time. Here, we prove a global synchronization theorem for a simple model of such swarmalators where the units move on a 1D ring. This can be thought of as a generalization from oscillators connected on random networks to oscillators connected on temporal networks, where the edges are determined by the oscillators' movements.

We investigate the first passage time beyond a barrier located at b≥0 of a random walk with independent and identically distributed jumps, starting from x0=0. The walk is subject to stochastic resetting, meaning that after each step the evolution is restarted with fixed probability r. We consider a resetting protocol that is an intermediate situation between a random walk (r=0) and an uncorrelated sequence of jumps all starting from the origin (r=1) and derive a general condition for determining when restarting the process with 0

This paper investigates the directed transport of particles in a coupled fractional-order system excited by Lévy noise. Numerical simulations reveal the effects of fractional order, Lévy noise and coupling coefficients on the directed transport. It is found that there exists an optimal fractional order, which maximizes the directed transport of particles. The optimal fractional order for the directed transport shifts to the left or right with different noise parameters, which means that the appropriate fractional order and noise parameters should be taken into account to maximize the directed transport. Meanwhile, the increase of the scale and symmetry parameters intensifies the directed transport of the particles, while the increase of the stability index suppresses the directed transport, so appropriate Lévy noise parameters will effectively amplify the directed transport. In addition, strong coupling can also effectively promote the directed transport of particles. These studies may provide a theoretical basis for the design of nanomachines, improving drug delivery across cell membranes and treating diseases of the nervous system.

In this paper, we study the problem of distributed generalized stochastic Nash equilibrium seeking for robot systems over a connected undirected graph. We use the cost functions containing uncertainty to represent the system's performance under varying conditions. To mitigate the challenges posed by this uncertainty, we employ the Tikhonov regularization scheme, which also helps us to relax the strongly monotone condition of the cost functions to the strictly monotone condition. We also consider the inequality constraints, which represent the feasible working space of robots. Additionally, auxiliary parameters are introduced in the control laws to facilitate seeing the variational generalized stochastic Nash equilibrium. The convergence of the proposed control laws is analyzed by using the operator splitting method. Finally, we demonstrate the effectiveness of the proposed algorithm through an example involving multiple robots connected through a communication network.